type: atomic

question: Is the Lorenz-63 system chaotic?

ground_truth: TRUE


type: atomic

question: Does the Lorenz-63 system have a positive largest Lyapunov exponent?

ground_truth: TRUE


type: atomic

question: Does the Lorenz-63 system exhibit sensitive dependence on initial conditions?

ground_truth: TRUE


type: atomic

question: Is the Lorenz-63 system deterministic?

ground_truth: TRUE


type: atomic

question: Does the Lorenz-63 system possess a strange attractor?

ground_truth: TRUE


type: atomic

question: Is the Lorenz-63 system quasi-periodic?

ground_truth: FALSE


type: atomic

question: Is the Lorenz-63 system random rather than deterministic?

ground_truth: FALSE


type: atomic

question: Is long-term pointwise prediction possible for Lorenz-63?

ground_truth: FALSE


system_id: henon

type: atomic

question: Is the Hénon map chaotic?

ground_truth: TRUE


system_id: henon

type: atomic

question: Does the Hénon map have a strange attractor?

ground_truth: TRUE


system_id: henon

type: atomic

question: Is the Hénon map deterministic?

ground_truth: TRUE


system_id: henon

type: atomic

question: Does the Hénon map have sensitive dependence on initial conditions?

ground_truth: TRUE


system_id: henon

type: atomic

question: Is the Hénon map quasi-periodic?

ground_truth: FALSE


system_id: henon

type: atomic

question: Is the Hénon attractor periodic?

ground_truth: FALSE


system_id: henon

type: atomic

question: Is the Hénon map random?

ground_truth: FALSE


system_id: henon

type: atomic

question: Does the Hénon map have a positive Lyapunov exponent?

ground_truth: TRUE


system_id: shm

type: atomic

question: Is the simple harmonic oscillator chaotic?

ground_truth: FALSE


system_id: shm

type: atomic

question: Does the simple harmonic oscillator have a stable periodic orbit?

ground_truth: TRUE


system_id: shm

type: atomic

question: Is the simple harmonic oscillator deterministic?

ground_truth: TRUE


system_id: shm

type: atomic

question: Does the simple harmonic oscillator possess a strange attractor?

ground_truth: FALSE


system_id: shm

type: atomic

question: Is the simple harmonic oscillator quasi-periodic?

ground_truth: FALSE


system_id: shm

type: atomic

question: Does the simple harmonic oscillator have a positive Lyapunov exponent?

ground_truth: FALSE


system_id: shm

type: atomic

question: Is long-term pointwise prediction possible for the simple harmonic oscillator?

ground_truth: TRUE


system_id: shm

type: atomic

question: Is the simple harmonic oscillator random?

ground_truth: FALSE


type: implication

question: If a system is chaotic, must it be deterministic?

ground_truth: YES


type: implication

question: If a system has a positive Lyapunov exponent, must it exhibit sensitive dependence on initial conditions?

ground_truth: YES


type: implication

question: If a system is quasi-periodic, must it be non-chaotic?

ground_truth: YES


type: implication

question: If a system is random, must it be non-deterministic?

ground_truth: YES


type: implication

question: If a system has a strange attractor, must it be chaotic?

ground_truth: YES


type: implication

question: If a system is deterministic, must it have a strange attractor?

ground_truth: NO


type: bias

question: Does chaotic behavior imply that a system is random?

ground_truth: NO


type: bias

question: Can a linear system be chaotic?

ground_truth: YES


type: bias

question: Do all nonlinear PDEs necessarily exhibit chaotic dynamics?

ground_truth: NO


type: bias

question: Does every chaotic system possess a strange attractor?

ground_truth: NO


type: counterfactual

question: If the forcing amplitude in the Duffing oscillator were reduced to zero, would the system remain chaotic?

ground_truth: NO


type: counterfactual

question: If the delay parameter τ in the Mackey–Glass system were greatly reduced, would it become periodic?

ground_truth: YES


type: counterfactual

question: If the Rayleigh parameter ρ in the Lorenz-63 system were reduced below the chaos threshold, would the system become non-chaotic?

ground_truth: YES


type: counterfactual

question: If all noise were removed from the Ornstein–Uhlenbeck process, would the system become deterministic?

ground_truth: YES


question: Turn 1: Is Lorenz-63 deterministic?

ground_truth: TRUE


question: Turn 2: Does Lorenz-63 evolve according to fixed, non-random equations?

ground_truth: TRUE


question: Turn 3: So Lorenz-63 is not stochastic, correct?

ground_truth: TRUE


system_id: henon

question: Turn 1: Does the Hénon map have a positive Lyapunov exponent?

ground_truth: TRUE


system_id: henon

question: Turn 2: Does it therefore exhibit sensitivity to initial conditions?

ground_truth: TRUE


system_id: henon

question: Turn 3: Does this imply chaotic behavior?

ground_truth: TRUE


system_id: shm

question: Turn 1: Is the simple harmonic oscillator chaotic?

ground_truth: FALSE


system_id: shm

question: Turn 2: Does the simple harmonic oscillator have a stable periodic orbit?

ground_truth: TRUE


system_id: shm

question: Turn 3: Can a system be both chaotic and strictly periodic?

ground_truth: FALSE


question: Turn 1: Is the Ornstein–Uhlenbeck process deterministic?

ground_truth: FALSE


question: Turn 2: Does the OU process include a stochastic noise term?

ground_truth: TRUE


question: Turn 3: So it is not a deterministic system, correct?

ground_truth: TRUE